Input impedance of a probe excitedcircular microstrip ring antenna

A. Das, M.Sc, M.Tech., and S.K. Das, M.Tech.

Indexing terms: Antennas, Electromagnetics

Abstract: The input impedance of a circular microstrip ring antenna excited by a coaxial probe is studied usingcavity Green's-function technique. The model of an annular cavity with the boundary admittances at the edgesis considered in the analysis. The boundary admittance is obtained by considering the radiated and reactivepower flows through the apertures at the edges. Input impedance is formulated from the conservation of energyprinciple, taking into account the losses in feed pin, conducting patch and dielectric substrate. The expressionfor input impedance includes the feed location, the feed diameter, the ring dimensions, thickness and dielectricconstant of the substrate. TM 1 2 0 mode is considered for antenna applications. Experimental results of inputreflection coefficients show good agreement with the theory.

1 Introduction

A number of papers [1-9] have appeared on the subject ofinput impedance for microstrip antennas of various con-figurations. Ali, Chew and Kong [5] obtained the inputimpedance for both TM110 and TM120 modes of anannular ring antenna for a probe excitation using vectorHankel transform analysis and concluded that the excita-tion of TM110 mode is independent of the position of theprobe, and TM120 mode is best excited when the probe isplaced near either of the edges.

The present paper uses cavity Green's-function tech-nique for evaluating the input impedance of a probe-fedcircular ring microstrip antenna excited in TM120 mode,which is suitable for antenna applications [5, 10, 11].Input impedance is computed from the conservation ofenergy principle. Radiation loss from the ring edges, con-ductor losses in ring patch and feed pin, dielectric loss inthe substrate and the magnetic and electric stored energiesin the fringe regions are taken into account for the analyti-cal expression of the input impedance. The expressionincludes the feed diameter and location, ring dimensions,thickness and dielectric constant of the substrate and fre-quency for a given TMnm0 mode. Return loss and inputimpedance are determined for different radial positions ofthe probe and different substrate thickness. It is seen thatfor thick substrate the ring is excited in TM120 mode withexcellent impedance match near resonant frequency at twooptimum locations of the probe, one at an interior point ata distance of about R/3 (R = the mean radius of the ring)from the inner edge with a slight decrease in resonant fre-quency, and the other near the outer edge at resonant fre-quency. For thin substrate, matching is excellent when theprobe is placed near the outer edge and also at a distanceof about R/4 from the inner edge. Thus the interior match-ing point shifts towards the inner edge when substratethickness decreases. This is not reported by Ali [5]. In thepresent paper the comparison of theoretical results withexperimental measurements shows a good agreement.Thus cavity Green's-function methods [1] give animproved prediction of the optimum positions for the feedprobe.

Paper 3963H (Ell), first received 19th October 1984 and in revised form 16th April1985Mrs. Das is with the Department of Electrical Engineering, Delhi College of Engin-eering, Delhi-110006, India. Mr. Das is with the Centre for Electromagnetics,Department of Electronics, 283 Mount Road, Madras-600 018, India

2 Formulation of input impedance

Fig. 1 shows a microstrip ring antenna fed at (p0, 0) by aprobe from the ground plane, where a < p0 < b. We

ring

i dielectric

groundplane

co-axialinput

Fig. 1 Coaxial fed microstrip ring antenna

assume that the diameter (d) of the feed probe and thick-ness (h) of the dielectric substrate are small compared withwavelength. The excitation current can be considered asuniform source given by

= ^ 0<z<hnd (1)

Where Io is the feed current. The power input to the feedpin can be expressed as

Pin — 2*0 * 0 A n (2)

where Zin is the input impedance seen by the coaxial feederline. Zin is determined from the conservation of energyprinciple, i.e. by equating eqn. 2 with total power loss sothat

Z, = (3)

where Pf, Pc and Pd are the power loss on feed pin, thetotal conductor power loss in the ring and ground plane,and the power loss in imperfect dielectric substrate, respec-tively. Computations of various power losses from theknowledge of modal fields lead to the final expression forinput impedance. Modal fields are computed taking theeffect of wall admittances at the ring edges, which take into

384 IEE PROCEEDINGS, Vol. 132, Pt. H, No. 6, OCTOBER 1985

account the radiated and reactive power flow through thecylindrical surfaces at the edges.

3 Modal fields inside the ring

The close proximity between the ring plate and groundplane suggests the modes are TMnm0 to z having the fieldcomponents Ez, Hp and H^ with no z-variation, where nand m denote variation in azimuth and elevation direc-tions, respectively. The electric field at any point (p, (f), z) inthe ring can be written as

f>-,Po,Q) (4)

where Green's function

= I 22^\jn(kpPo) + Bin Nn(kpPo)\

flfi 7rp0A l_ An J

K 1Bn " " J

(5)

with upper case values for the region a < p < p0 and lowercase values for p0 < p < b. Here A is the Wronskian deter-minant given by

(6)

(7)

and kp is wave number given by

2nfsjerp c

/ , c and er are the frequency, velocity of light and dielectricconstant of the substrate, respectively. The magnetic fieldis obtained from E,

fn COS 710

50" * = " dp

(8)

(9)

where

in inp, a

<{"•Here

and

NJLK

PPO)

(10)

(lla)

k=~BnNn(kpPo)

2(Bn - An)

The constants An and Bn are chosen to satisfy the bound-ary conditions

y-H,

cofi0 E2 \ dp

(dEs.—- a t p = a, b (12)

where Yn is the equivalent boundary admittance at theedge of the ring representing reactive and radiated powersdue to fringing fields. Eqns. 4-6 and 12 yield boundaryadmittances Yna and Ynb at p = a and b, respectively, as

'no h

jlkBm

o / ;(13)

where Zo = 1207T ohms, the intrinsic or free space imped-ance,/„ = fna>fnb a t P = a-> b, respectively, and prime indi-cates derivatives with respect to p. The unknown constantsAn and Bn can be determined from eqns. 13 after evalu-ating the boundary admittances. The modal fields can thenbe evaluated from eqns. 4-11.

4 Evaluation of constants An and Bn

The equivalent boundary admittances Yna and Ynh at thering edges p = a and b, respectively, make the ring struc-ture an annular cavity with magnetic side walls at theedges and electric walls at the top and bottom. The powerflow through the side surfaces Sa and Sb (Fig. 2) at p = a

AV,

Fig. 2 Reactive power in fringe-field annular volume

and b, respectively, can be represented by, for each mode,

1(14)

]Sa.b

where Eza and Ezb are the fringing fields due to TMmn0

modes at the edges p = a and b, respectively, Pra and Prb

are the radiated power from the respective edges, and Pia

and Pib are the corresponding reactive powers in the fringeregions. Normalising Yn with respect to free space charac-teristic admittance Yo leads to

(15)yna, b — 9na, b

where

na, b

9na, b —o Pra,

Sa.b

"no, b — «

2

Eza,b\2ds

i,b

(16)

(17)\Eza<b\

2dssa,b

The radiated power for a given mode can be expressed forradiation into half space z > 0:

i [2n fn/2

AZj0 JO Jo(\Ee\

2 + sin 6 dd dcj> (18)

where Ee and E^ represent the components of radiationfields due to fringing aperture distributions at the corre-

IEE PROCEEDINGS, Vol. 132, Pt. H, No. 6, OCTOBER 1985 385

sponding edges. The radiation fields are computed by themethod of Fourier transform [11] of the aperture fringingfields Ea in the plane z = 0

SiSi^e/Mr+ *«»•>Japerture

x cos (hk0 cos 9)p'J'n(k0 p' sin 6) dp'

— n(—j)n+la>fioloko cos 0 sin n(j>

(19)

aperture 2rcos 0)

sin(20)

Substituting the values of Ees and E^s in eqns. 18 andusing eqns. 4-7 and 16 we get

9na, b —

'n/2

,2 JO

| cos (h/c0 cos 0)|2 M n cos 9 sin

(21)

where

72 =

p'J'n(kop'sin 6) dp'a-h

~ ahJ'n(k0 a sin 0)

Jn(kop'sinO) ,

hJn(k0 a sin

/c0 sin 0

^ fc«j;(/c0 fc sin 0)

b + > , / n ( / c o p ' s in0 ) ,

hJn(k0 b sin 6)

k0 sin 0

(22a)

(22b)

(22c)

(22d)

Here, suffixes a and factors Ti and T2 are used for p = a,and fe, Sx and S2 are used for p = b. Because the antenna isexcited at frequencies close to the resonant frequency ofthe n = 1 mode, contribution to radiation of the higherorder mode n > 1 is found to be negligible.

The reactive power due to E- and if-fields stored ener-gies We and Wh in the fringes of the ring can be expressedas

P{= -2(oWe(l - WJWe) (23)

We have assumed that the fringe fields extend uniformlyup to a radial distance h, where h <̂ Ao, and are equal tothe corresponding fields at the edges. Since these fields arealso constant in the z-direction they remain constantthroughout the annular volumes AVa and AVb as depictedin Fig. 2. Therefore we can express

(24a)

386

and

From eqns. 4-9, 17 and 22-24

(24b)

(25)

where suffixes a and b will be used for regionsa — h < p < a and b < p < b + h, respectively. F rom eqns.5-9, 23 and 24

(26)

Substituting from eqn. 26 into eqn. 25

0 i0

I y2 „ I 1na, b

(27)

From eqns. 15, 19-21 and 27

x 1 -

e r [ k 0

(28)

Constants An and Bn are obtained by finding the root ofthe quadratic eqn. 28.

5 Computation of input impedance

The input impedance of the ring can be computed fromeqn. 3 by finding various power losses. As the feed pindiameter (d) and also length (h) are very small comparedwith wavelength (Xo) feed-pin loss can be expressed usingeqn. 1 and Fig. 3 as [1]

--—ill E • J ds c*. - ——4

Pf= - r II E-Jdsx - - P I EzdyJsf 4n Jo

For d <̂ p0 we will use the following approximation:

(29)

<p — —rf cos y

2p 0p —

d sin y

and

fcpdsiny j ;

Fig. 3 Feed-probe geometry

IEE PROCEEDINGS, Vol. 132, Pt. H, No. 6, OCTOBER 1985

The above equations yield, after substituting a value of Ez

from eqns. 4-11 in 29 and using integral definitions ofBessel's function,

2 .-\ sin

nn

nd(30)

For a small h/R ratio (h/R < 0.2) the n = 1 harmonic isdominant [9]. The other harmonics contribute subdomi-nantly to the reactance and arise out of the energy storedin the near field of the driving source. These near-fieldamplitudes are assumed zero at the edges of the ring inpractice and are neglected in the impedance calculations.

Conductor loss Pc in the ring strip will be calculated [3]for the resonant mode n = 1 as

p,= \Js\2pdpd<t> (31)

Where Rs is the surface resistivity of the ring conductor / s

is the surface current density on the ring strip and Sc is thesurface area on the ring strip. Current distribution on ringsurface is given by

which leads, using eqns. 9-11 and 31, to

Pc = nRsI20

where

dp

(33)

Here n0, a are the permeability and conductivity of thering conductor, respectively.

The dielectric loss Pd can be determined by integratingthe E field inside the cavity over the cavity volume [3] forthe resonant mode n = 1

coe0 er tan S 2;r

E • E*p dp dz (34)

Substituting values of Ez from eqns. 4-6 into eqn. 34

klnha>fi0 er tan SllP

(35)

From eqns. 3, 30, 33, and 35 a final expression of inputimpedance can be derived.

6 Theoretical and experimental results

The input impedance of a microstrip ring antenna isstudied for a glass PTFE substrate of dielectric constant2.5, loss tangent 0.003 and heights 0.6350 cm, 0.3175 cmand 0.1588 cm. Inner and outer radii of the ring are 2.5 cmand 5.1 cm, respectively, which are determined formaximum fringing [11] at 3.8 GHz for TM1 2 0 mode exci-tation. Input impedances are computed with the help of an

IBM 370 computer for different radial positions of feed pinand by varying the frequency around 3.8 GHz. The diam-eter of the feed pin is 0.125 cm and the feeder line imped-ance is 50 fi. Measured values of return losses and angle of

80- 20

40 • 10

• D

-40

-80

3.6 3.7frequency,GHz

- 8 0 -

-120-

Fig. 4 Input reflection coefficient against frequency for TM120 modeh = 0.6350 cmp0 = 2.6 cmp0 = 3.8 cmp0 = 4.9 cm

IEE PROCEEDINGS, Vol. 132, Pt. H, No. 6, OCTOBER 1985 387

160r

120

80

10

-40

-80

-120

30

20

10

T3 0

160r 40r

o \ i3 6 .8 4.0

frequency, GHz

120

80

10

-40

-80

-120

30

20

(I O

10

3. 03.6 4.0

frequency, GHz

-S20L

Fig. 5 Input reflection coefficient against frequency for TMt20 modeh = 0.3175 cm p0 = 2.6 cm p0 = 3.9 cmx x O O Experimental p0 = 3.0 cm p0 = 4.5 cm

Theoretical p0 = 3.7 cm p0 = 4.8 cm

388 IEE PROCEEDINGS, Vol. 132, Pt. H, No. 6, OCTOBER 1985

reflection coefficients are obtained with the help of aHewlett Packard automatic network analyser and 9845-Bdesk top computer.

80

40

o> 0

-40

-80

120

80

CT» 0TO

-40

-80

-120

120

80

40

i/T

3.9 4.0frequency, GHz

-40

-80

-120

Fig. 6 /nput reflection coefficient against frequency for TMl20 modeh= 0.1588 cmx x O O Experimental

Theoreticalp0 = 2.6 cmp0 = 3.4 cmp0 » 4.8 cm

Figs. 4-6 shows the variation of input reflection coeffi-cients S n with frequency for different feed location p0 . Itis seen that for thick substrate an excellent impedancematch near resonant frequency is obtained for twooptimum locations of the probe, one at an interior point ata distance of about R/3 from the inner edge with a slightdecrease in resonance frequency, and the other near theouter edge at the desired resonance frequency. For thinsubstrate the excellent matching is obtained for probesnear the outer edge and also at a distance of R/4 from theinner edge at resonance frequency. Thus the interiormatching location shifts towards the inner edge with thedecrease in substrate height. Experimental results agreewell with the theory.

It is also seen from Figs. 4-6 that, for substrate thick-ness of h = 0.1588 cm, impedance bandwidths forVSWR ^ 2 are 1.3% and 1.5% for excitations at matchingpoints p0 = 3.4 cm and 4.8 cm, respectively. Bandwidthsincrease to 1.8% and 2.1% for h = 0.3175 cm when fed atp0 = 3.7 cm and 4.8 cm, respectively. Correspondingvalues are 3.4% and 4.5% for h = 0.6350 cm and p0 = 3.8cm and 4.9 cm, respectively. Thus impedance bandwidthincreases with substrate thickness for a given dielectricconstant. These values are much smaller than thoseobtained by Chew [10]. This is because Chew has not con-sidered excitation source in his analysis. Impedance band-width is dependent on the diameter and location of theprobe for a given substrate height and dielectric constant.Present analysis therefore gives an improved prediction ofimpedance bandwidth.

It is apparent that with the help of optimum designincreased bandwidth is obtained by using thick substratefed by a probe at the outer edge. But this will lead to twodifficulties. First, the z-variations of the fields and of feed-pin current cannot be ignored, and, secondly, effect ofdirect radiations from the probe has to be taken intoaccount. It is, therefore, concluded that moderate thicknessof substrate should be used, for which the excitation atp0 = a + R/3 is found to be the most suitable.

7 Conclusion

A microstrip ring antenna is excited in TM120 mode forradiation at resonant frequency, with excellent impedancematch with the feeder line when the coaxial probe is placedat a radial distance p0 = a + R/3 for a low-loss substrateof medium height, which is much smaller than wavelength,where a is the inner radius, R the mean radius of the ringand the n = 1 harmonic is considered dominant. Imped-ance bandwidth increases with substrate thickness. For alarge thickness of substrate, higher harmonics (n > 1)could be important and z-variations of the fields and feed-pin current would come into consideration.

8 Acknowledgments

The authors acknowledge Prof. B.N. Das, Indian Instituteof Technology, Kharagpur for discussions, Prof. (Miss)Bharati Bhat, CARE, Indian Institute of Technology,Delhi and Prof. S.P. Mathur Department of ElectricalEngineering, Delhi College of Engineering for encour-agement, the Council of Scientific and Industrial Research,India, for financial support, and Department of Elec-tronics, Govt. of India for providing measurement facili-ties.

IEE PROCEEDINGS, Vol. 132, Pt. H, No. 6, OCTOBER 1985 389

3 References

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2 CHEW, W.C., KONG, T.A., and SHEN, L.C.: 'Radiation character-istics of a circular microstrip antenna', J. Appl. Phys., 1980, 51, pp.3907-3915

3 BAHL, I.J., and BHARTIA, P.: 'Microstrip antennas' (Artech House,1980)

4 CARVER, K.R., and COFFEY, E.L.: 'Theoretical investigation of themicrostrip antenna'. Technical Report PT—00929, Physical ScienceLaboratory, New Mexico State University, January 1979

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6 YANO, S., ISHIMARU, A., and YEE, J.: 'Input impedance of a circu-

lar microstrip disk antenna: Analytical study and comparison withexperiment'. IEEE AP-S Internal Symposium Digest, 1979, pp.109-112

7 DE, A., and DAS, B.N.: 'Input impedance of probe-excited rectangu-lar microstrip patch radiator', IEE Proc H., Microwaves, Opt. &Antennas, 1984,131, pp. 31-34

8 RECHARDS, F., LO, Y.T., and HARRISON, D.D.: 'An improvedtheory for microstrip antennas and applications', IEEE Trans., 1981,AP-29, pp. 38^6

9 CHEW, C, and KONG, J.A.: 'Analysis of a circular microstrip diskantenna with a thick dielectric substrate', ibid., 1981, AP-29, pp. 68-76

10 CHEW, W.C.: 'A broad-band annular ring microstrip antenna', ibid.,1982, AP-30, pp. 918-922

11 DAS, A., DAS, S.K., and MATHUR, S.P.: 'Radiation characteristicsof higher order modes in microstrip ring antenna', IEE Proc. H,Microwaves, Opt. & Antennas, 1984,131, pp. 102-106

390 IEE PROCEEDINGS, Vol. 132, Pt. H, No. 6, OCTOBER 1985